To make a quiche, you need 1 tablespoon of butter for every 6 eggs. Write a ratio that compares these two quantities. Which ratios are equivalent to this ratio? Check all that apply.

A. [tex]\frac{12 \text{ eggs }}{2 \text{ tbsp }}[/tex]

B. [tex]\frac{15 \text{ eggs }}{3 \text{ tbsp }}[/tex]

C. [tex]\frac{24 \text{ eggs }}{4 \text{ tbsp }}[/tex]

D. [tex]\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}[/tex]

We are given that the recipe calls for 1 tablespoon of butter for every 6 eggs. This means that the ratio of eggs to tablespoons of butter is

[tex]$$\frac{6 \text{ eggs}}{1 \text{ tbsp}}.$$[/tex]

Now, we need to check which of the following ratios are equivalent to this ratio.

1. For the ratio

[tex]$$\frac{12 \text{ eggs}}{2 \text{ tbsp}},$$[/tex]

we calculate:

[tex]$$\frac{12 \text{ eggs}}{2 \text{ tbsp}} = 6 \text{ eggs per tbsp}.$$[/tex]

This ratio is equivalent to the original ratio.

2. For the ratio

[tex]$$\frac{15 \text{ eggs}}{3 \text{ tbsp}},$$[/tex]

we calculate:

[tex]$$\frac{15 \text{ eggs}}{3 \text{ tbsp}} = 5 \text{ eggs per tbsp}.$$[/tex]

This is not equivalent to the ratio of 6 eggs per tablespoon.

3. For the ratio

[tex]$$\frac{24 \text{ eggs}}{4 \text{ tbsp}},$$[/tex]

we calculate:

[tex]$$\frac{24 \text{ eggs}}{4 \text{ tbsp}} = 6 \text{ eggs per tbsp}.$$[/tex]

This ratio matches the original ratio.

4. For the ratio

[tex]$$\frac{9 \text{ eggs}}{1.5 \text{ tbsp}},$$[/tex]

we calculate:

[tex]$$\frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = 6 \text{ eggs per tbsp}.$$[/tex]

This is also equivalent to the original ratio.

Thus, the ratios equivalent to the original ratio [tex]$6 \text{ eggs} : 1 \text{ tbsp}$[/tex] are from options 1, 3, and 4.